Question: Solve for $x$ and $y$ using elimination. ${2x+2y = 38}$ ${2x-3y = -7}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the bottom equation by $-1$ ${2x+2y = 38}$ $-2x+3y = 7$ Add the top and bottom equations together. $5y = 45$ $\dfrac{5y}{{5}} = \dfrac{45}{{5}}$ ${y = 9}$ Now that you know ${y = 9}$ , plug it back into $\thinspace {2x+2y = 38}\thinspace$ to find $x$ ${2x + 2}{(9)}{= 38}$ $2x+18 = 38$ $2x+18{-18} = 38{-18}$ $2x = 20$ $\dfrac{2x}{{2}} = \dfrac{20}{{2}}$ ${x = 10}$ You can also plug ${y = 9}$ into $\thinspace {2x-3y = -7}\thinspace$ and get the same answer for $x$ : ${2x - 3}{(9)}{= -7}$ ${x = 10}$